Prosecutors dropped two more serious charges that Heard illegally imported the Yorkshire terriers, Pistol and Boo, into the country last year, when Depp was filming the fifth movie in the "Pirates of the Caribbean" series. A conviction on the illegal importation counts could have sent the actress to prison for up to 10 years.

The false documents charge carries a maximum penalty of a year in jail and a fine of more than 10,000 Australian dollars ($7,650). But Magistrate Bernadette Callaghan sentenced Heard instead to a one month good behavior bond. She will have to pay a AU$1,000 ($767) fine if she violates the conditions of the bond over the next month.

Heard's lawyer, Jeremy Kirk, told the Southport Magistrates Court on Queensland state's Gold Coast that his client never meant to lie on her incoming passenger card by failing to declare she had animals with her. In truth, Kirk said, she was simply jetlagged and assumed her assistants had sorted out the paperwork.

Prosecutor Peter Callaghan said ignorance and fatigue were no excuse.

"The laws apply to everyone," he said.

The debacle over the dogs began last May, when Agriculture Minister Barnaby Joyce accused Depp of smuggling the tiny terriers aboard his private jet when he returned to Australia to resume filming the "Pirates" movie.

Australia has strict quarantine regulations to prevent diseases such as rabies from spreading to its shores. Bringing pets into the country involves applying for a permit and quarantine on arrival of at least 10 days.

"If we start letting movie stars -- even though they've been the sexiest man alive twice -- to come into our nation (with pets), then why don't we just break the laws for everybody?" Joyce said at the time. "It's time that Pistol and Boo buggered off back to the United States."

Depp and Heard were given 72 hours to send Pistol and Boo back to the U.S., with officials warning that the dogs would otherwise be euthanized. The pooches boarded a flight home just hours before the deadline ran out.

The comments by Joyce, who is now the deputy prime minister of Australia, elevated what might otherwise have been a local spat into a global delight for comedians and broadcasters. One newspaper ran a doggie death countdown ticker on its website that marked the hours remaining before the dogs had to flee the country, and comedian John Oliver dedicated a more than 6-minute segment to lampooning the ordeal.

Depp himself poked fun at the drama during a press conference in Venice last year where he was asked if he planned to take the dogs for a gondola ride. "No," he replied. "I killed my dogs and ate them, under direct orders from some kind of, I don't know, sweaty, big-gutted man from Australia."

Depp and Heard made a videotaped apology that was played in court during Monday's hearing.

"If you disrespect Australian law," Depp says in the video, "they will tell you firmly."